H∞ deconvolution filter design for time-delay systems via equivalent transformation

This paper proposes an H∞ deconvolution design for linear systems with output state time delay. The basic idea of our study is to eliminate the time delays of system and transform it to a delay-free system by the bicausal change of coordinates approach. Then, we design H∞ deconvolution for the delay-free systems, which is equivalent to the original system with time delays. We analyze the general structure and innovation structure of the H∞ deconvolution filter. Based on the bounded real lemma, a time domain design approach and a sufficient condition for the existence of deconvolution filter are presented. The prarameterization of the deconvolution filter could be completed by solving a Riccati equation. The proposed method is useful for the case that does not require statistical information about disturbances.